182 LETTERS OX NATURAL MAGIC. 



of the axis A'B' as at A m C, while the part CB 

 is on the other side, as at C n B. Hence the 

 point C, being always pulled by equal and oppo- 

 site forces, remains at rest as if it were absolutely 

 fixed. This stationary point is called a node, and 

 the vibrating portions A 7 m C, C n B' loops. The 

 very same is true of the string A"B", the points 

 C and D being stationary points ; and upon the 

 same principle a string may be divided into any 

 number of vibrating portions. In order to prove 

 that the string is actually vibrating in these equal 

 subdivisions, we have only to place a piece of 

 light paper with a notch in it on different parts 

 of the string. At the nodes C and D it will 

 remain perfectly at rest, while at m or n in the 

 middle of the loops it will be thrown off or 

 violently agitated. 



The acute sounds given out by each of the 

 vibrating portions are called harmonic sounds, and 

 they accompany the fundamental sound of the 

 string in the very same manner as we have already 

 seen that the eye sees the accidental or harmonic 

 colours while it is affected with the fundamental 

 colour. 



The subdivision of the string, and consequently 

 the production of harmonic sounds, may be 

 effected without touching the string at all, and by 

 means of a sympathetic action conveyed by the 

 air. If a string AB, for example, Fig. 40, is at 

 rest, and if a shorter string A*C, one third of its 

 length, fixed at the two points A* and C, is set 

 vibrating in the same room, the string AB will 

 be set vibrating in three loops like A"B", giving 

 out the same harmonic sounds as the small string 

 A"C. 



